On a class of electrorheological fluids
The paper deals with flows of a class of electrorheological fluids governed by physical laws which include a nonconstant electrical field. Such a problem is analyzed in view of possible applications in modeling ``smart materials''. The authors deal with Newtonian fluids of dielectric type, whose mathematical study leads to a system of PDE, from which the electrical field can be derived by simply solving Dirichlet problem for a quasilinear elliptic equation. As a consequence, the authors obtain a global existence of weak solution for arbitrary \(L^2\) initial data and under some technical assumptions on the force and electric field. Such solution is shown to be unique in two-dimensional case. In three-dimensional case, for initial velocity in \(H^1\), a regular local (unique) solution is obtained which, in turn, is shown to be global in time under some smallness assumption on the data.
scientific article; zbMATH DE number 1898304